1. Field of the Invention
This invention relates generally to a method and apparatus for interpolating digital data and, more particularly, to interpolating defective data generated during transmission of digital data obtained by performing 1-bit digitization.
2. Description of the Background
The method of recording, reproducing and transmitting digital signals converted from analog signals has hitherto been practiced in the field of recording and/or reproducing apparatus employing an optical disc, such as a compact disc (CD), or a magnetic tape, such as a digital audio tape (DAT), or digital broadcasting, such as satellite broadcasting. In the conventional digital audio transmission apparatus, described above, the sampling frequency of 48 kHz or 44.1 kHz and 16 quantization bits have been prescribed as a format for conversion of the analog signals into digital signals.
With the above-described digital audio transmission apparatus, however, the number of quantization bits of the digital audio data generally determines the dynamic range of the demodulated audio signals. For transmitting high-quality audio signals it is necessary to increase the number of quantization bits from the current 16 bits to 20 or 24 bits. Once the number of quantization bits is fixed at a pre-set value, the signal processing system is correspondingly designed, the number of quantization bits cannot thereafter be increased and high-quality audio signals cannot be output from the conventional apparatus.
One method for digitizing audio signals is known as sigma-delta (.SIGMA..increment.) modulation and was proposed by Y. Yamazaki in "AD/DA Converter and Digital Filter", J. of Japan Society of Acoustics, Vol. 46, No. 3 (1990), pages 251 to 257.
FIG. 8 shows the construction of a 1-bit .SIGMA..increment. modulation circuit. In this circuit the input audio signals are supplied at an input terminal 91 and fed via an adder 92 to an integration circuit 93. An output signal from the integrator 93 is supplied to a comparator 94 where it is compared to a neutral point potential of the input audio signal, not shown, so as to be quantized by one bit every sampling period. The frequency of the sampling period, that is, the sampling frequency, is 64 or 128 times the conventional frequency of 48 kHz or 44.1 kHz. The quantization may be 2-bit or 4-bit quantization, instead of the 1-bit quantization of this example.
The quantized data is supplied to a one-sample delay unit 95 and thereby delayed by one sampling period. The delayed data is converted by, for example, a 1-bit D/A converter 96 into an analog signal which is supplied to the adder 92 where it is added to the input audio signal fed in at the input terminal 91. The quantized data output by the comparator 94 is taken out at an output terminal 97. Consequently, with the sigma-delta (.SIGMA..increment.) modulation, performed by the .SIGMA..increment. modulation circuit, audio signals of a broader dynamic range can be obtained, even with a number of quantization bits as small as one bit, by setting the sampling frequency to a sufficiently higher value. In addition, a sufficiently broad range of transmission may be assured.
On the other hand, the .SIGMA..increment. modulation circuit structure lends itself to integration, and high A/D conversion precision may be achieved rather easily, so that it is extensively used within A/D converters. The .SIGMA..increment. modulated signal can be restored to an analog audio signal by being passed through a simplified analog low-pass filter. By taking advantage of these characteristics, the .SIGMA..increment. modulation circuit may be applied to a recorder handling high-quality data, or to a high-quality data transmission system.
In the above-described digital audio data, if trouble occurs in the transmission system and bad data is produced, the data is fixed at "1" or "0". In digital audio data, continuous "1"s or "0"s correspond to a positive maximum value and a negative maximum value of the demodulated signal, respectively. For example, if part of the signal becomes defective in the transmission system, the maximum level noise is produced in the defective portion, thus possibly destroying a monitor amplifier or speaker.
Thus, in a CD or DAT for which the format for 16 bits is prescribed as the number of quantization bits, the signal format is set so that the continuous "1"s or "0"s assume an intermediate value in the demodulated signal without becoming a maximum level. Therefore, even if defective data is produced as described above, there is no risk of generation of the maximum noise level. Also, an error correction code is provided in the data so that data errors, if any, may be concealed to a pre-set extent. For data defects exceeding the ability of the error correction code, data lying ahead of or behind the defective data are used for interpolation, or data that is directly ahead of the defective data is held, in order to possibly avoid problems in connection with the listener's auditory sense.
For such interpolation, processing employing linear interpolation, as shown for example in FIG. 9, is performed. In FIG. 9, interpolated data D.sub.n, where n is an integer from 1 to N, is found by the following equation (1): EQU D.sub.n =D.sub.A +n.times.(D.sub.B -D.sub.A)/N (1)
where N is the number of bad data, D.sub.A is data directly before the bad data, and D.sub.B is data directly following the bad data.
With .SIGMA..increment. modulation, however, since the word length of each data is short and is equal to 1 bit, for example, interpolation employing the preceding data or the succeeding data as described above cannot be made. Thus, a method known as the pre-hold method may be employed that consists of replacing the defective data portion by a block of the previous data of the same length as the defective data portion. This method is shown in FIG. 10, however, this method cannot be said to be completely useful however since the junction point is occasionally not smooth and an extremely large noise tends to be produced.
It may also be envisaged to transform data resulting from the above-mentioned .SIGMA..increment. modulation into data of the conventional signal format for CD or DAT using a decimation filter. If the modulated data is transformed into data of the conventional signal format as described above, it becomes possible to avoid any problem in connection with the human hearing mechanism by performing interpolation in the same way as conventionally or by holding the directly preceding data. The characteristics of the processed signals are assimilated to those of the conventional CD or DAT, however, so that the characteristics proper to the .SIGMA..increment. signals, such as broad bandwidths or high dynamic range, cannot be exploited.
Thus, if bad data is produced due to troubles in the transmission system, there is no means available in .SIGMA..increment. modulation for concealing the errors by interpolation, for example, so that it has been extremely difficult to exploit adequately the advantages of .SIGMA..increment. modulation in the usual transmission system.